Sinc function doesnt look good

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Bruce Pollom
Bruce Pollom on 15 Jan 2018
Hello so I have the code below :
clear all;
clc;
Fs = 100;
Ts = 1/Fs;
t=-1:Ts:1;
%u(t-0.5)
step = zeros(size(t));
step(t>0.5) = -1;
figure
grid
subplot(3,2,1)
plot(t,step)
title ('u(t-0.5)')
%u(t+0.5)
step2 = zeros(size(t));
step2(t>-0.5)= 1;
grid
subplot(3,2,2)
plot(t,step2)
title ('u(t+0.5)')
xt=step2+step;
dt = 1/100;
grid
subplot(3,1,3)
plot(t,xt)
title ('u(t+0.5)-u(t-0.5)')
y = conv(xt,xt)*dt;
t3 = -2 :Ts:2;
grid
figure
subplot(2,1,1)
plot(t3,y)
title('first convo')
z = conv (y,xt )*dt;
t4= -3:Ts:3;
dw=1/100;
grid
subplot(2,1,2)
plot(t4,z)
title('second convo')
q = conv(z,xt)*dt;
t5 = -4:Ts:4;
grid
figure
plot(t5,q)
title('third convo')
nfft1=length(xt)*32;
XT=fft(xt,nfft1)*dw;
XT=fftshift(XT);
F=-Fs/2:Fs/nfft1:Fs/2-Fs/nfft1;
grid
figure
plot(F,abs(XT));
title('xt in freq')
nfft2=length(y)*32;
Y = fft(y,nfft2)*dw;
Y = fftshift(Y);
F=-Fs/2:Fs/nfft2:Fs/2-Fs/nfft2;
grid
figure
plot(F,abs(Y))
title('first convolution in freq')
nfft3=length(z)*32;
Z=fft(z,nfft3)*dw;
Z=fftshift(Z);
F=-Fs/2:Fs/nfft3:Fs/2-Fs/nfft3;
grid
figure
plot(F,abs(Z))
title('second convolution in freq')
nfft4=length(q)*32;
Q=fft(q,nfft4)*dw;
Q=fftshift(Q);
F=-Fs/2:Fs/nfft4:Fs/2-Fs/nfft4;
grid
figure
plot(F,abs(Q))
title('third convolution in freq')
XT is a sinc function as it turned out on paper but when I plot it it doesnt look like a sinc function . Is the code wrong or is it right and that's how it's supposed to look ?

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